On the relation between modal and multi-modal logics over Łukasiewicz logic

RICARDO O. RODRIGUEZ; LLUIS GODO; FRANCESC ESTEVA

Nápoles

Conferencia; FUZZIEEE2017; 2017

IEEE

In a previous paper, it was shown that the (minimal)modal logic MŁcn with fuzzy accessibility relations over thefinite-valued Łukasiewicz logic Łn and a corresponding multimodallogic mMŁcn (with a modality a for each value a in then-valued Łn-chain) had the same expressive power when thelanguage is extended with truth-constants. In this paper wepartially extend these results when replacing the underlyinglogic Łn by the infinite-valued Łukasiewicz logic (with rationaltruth constants in the language). We prove that the (standard)tautologies of the modal logic MŁc (resp. mMŁc) are in fact thecommon tautologies of all the logics MŁcn (resp. all the logics mMŁcn) when letting n vary over N. This fact opens the doorto show an alternative proof of the finite model property forthese logics and hence their decidability.